It happened on June 20, 1756. The nawab of Bengal, Siraj-ud-daulah, and his troops raided and captured British Fort William and the rest of Calcutta (now called Kolkata). The British who surrendered were put in a small (18 feet by 14 feet 10 inches/5.5 m by 4.3 m; with two small windows) lockup known as the "Black Hole" for the night. The next morning, of the 146 people (145 men and one woman) placed in the small room, only 23 had survived. The incident was considered evidence for the cruelties of the nawab.
The account of the incident was given by one of the survivors, a John Z. Holwell. A quote:
For we were no sooner all within the barracks, than the guard advanced to the inner arches and parapet wall, and with their muskets presented, ordered us to go into the room at the southernmost end of the barracks, commonly called the Black Hole prison.... Like one agitated wave impelling another, we were obliged to give way and enter; the rest followed like a torrent, few amongst us, the soldiers excepted, having the least idea of the dimensions or the nature of a place we had never seen....
Prior to the incident, the British only had a trading station and a fort (Fort William) in Calcutta. Relations between the nawab and the Governor were strained and made worse by the Governor's insistence on fortifying the city and garrison (with the help of the British East India Company) despite the nawab's request to cease and take them down. The British were preparing for the possibility of war (The Seven Years' War) and also backed the nawab's opposition. Since it seemed clear they would continue, Siraj-ud-daulah captured the city, taking the post at Cassimbazar on the way.
The Governor, much of his staff, and many other British were able to escape before the nawab and his men arrived. A small number did not, and after some measure of resistance, surrendered. That night, the prisoners were placed in the "Black Hole."
Things seem to break down there. There is no other primary firsthand account except from Holwell. And it appears that his numbers are inflated (it is nearly impossible to cram that many people into that space). Worse for him, he gives conflicting numbers. A month later he had reported that it was 165 or 170 people involved. A month after that, it was the 146 figure. (One of the Governor's men gave the numbers as 150, 22 survivors.) The number of women who (maybe) were involved is in dispute as well as certain descriptions of the size of the room. Or whether there was one or two windows. And remember, Holwell is the only substantial firsthand account. Nothing from the nawab's men or citizens of Calcutta, nothing from the other survivors (some later "verified" his account, though there were also discrepancies in details; some chose to remain silent).
While it is clear that a number of prisoners were placed in the room and it's highly likely some or even many died (though it is possible that a number of them were already wounded from the battle), the number can't be nailed down other than showing that the account is exaggerated (the nawab's part in the incident has been determined to be primarily of negligence, at most).
So how many?
Some scholars have put the number at no more than 69 (a few Indian scholars that deny it took place at all). Another study claims that it was around 64 with 21 survivors. Still another found that only about 43 British prisoners were unaccounted for and probably no more than 15 actually died.
Because of the ubiquity of Holwell's narrative and the emotional impact that sort of thing has, his version has become widely accepted as correct, despite findings over the last century suggesting otherwise. Sometimes a good (and useful, as propaganda for the British) story gets in the way of facts.
(Sources: a number of web sites, of particular help were www.britannica.com and www.the-week.com/20dec03/cover5.htm)